AMPL

AMPL (A Mathematical Programming Language) is a high-level language designed for modeling and solving large-scale optimization problems. It is widely used in operations research, mathematical optimization, and decision science.

Key Features of AMPL:

1. Algebraic Modeling Language – AMPL provides a concise way to express complex mathematical models using algebraic notation similar to traditional mathematical formulations.
2. Separation of Model and Data – Models and data are defined separately, allowing flexibility in solving different problem instances without modifying the core model.
3. Solver Independence – AMPL interfaces with various optimization solvers, such as CPLEX, Gurobi, and IPOPT, making it easy to switch between solvers.
4. Support for Various Optimization Problems – It can handle linear programming (LP), integer programming (IP), nonlinear programming (NLP), and mixed-integer programming (MIP) problems.
5. Ease of Use – AMPL has a simple syntax that allows users to formulate problems in a way that closely resembles mathematical notation.

Typical Workflow in AMPL:

1. Define the Model – Specify variables, objective functions, and constraints.
2. Provide Data – Input specific problem data separately.
3. Select a Solver – Choose an appropriate solver to process the model.
4. Run Optimization – Execute the model and solver to obtain results.
5. Analyze Results – Extract and interpret the solution.

Example AMPL Model (Linear Programming)

amplCopyEditset PRODUCTS;
param cost {PRODUCTS};
param demand {PRODUCTS};
var Make {PRODUCTS} >= 0;

minimize Total_Cost:
    sum {p in PRODUCTS} cost[p] * Make[p];

subject to Demand_Constraint {p in PRODUCTS}:
    Make[p] >= demand[p];

data;
set PRODUCTS := A B C;
param cost := A 5 B 4 C 6;
param demand := A 10 B 8 C 15;
end;

This simple example defines a production optimization problem where the objective is to minimize total cost while satisfying demand constraints.

AMPL is widely used in industries such as logistics, finance, energy, and supply chain management due to its flexibility and solver compatibility.